NEW W-Q,W-P(SL(2)) ALGEBRAS FROM THE ELLIPTIC ALGEBRA A(Q,P)((SL)OVER-CAP(2)(C))

We construct operators t(z) in the elliptic algebra A(q,p),((sl)over-c ap(2)(c)) closing an exchange algebra when p(m) = q(c+2) for m is an e lement of Z. In addition they commute when p = q(2k) for k non-zero in teger, and they belong to the center of A(q,p)((sl)over-cap(2)(c)) whe n k is odd. The Poisson structures obtained for t(z) in these classica l limits are identical to the q-deformed Virasoro Poisson algebra, cha racterizing the structures at p not-equal q(2k) as new W-q,W-p(sl(2)) algebras. (C) 1998 Elsevier Science B.V.